Let us now describe the
the deterministic ReLU neural network proposed in [1]}; its architecture is depicted in Figure REF .Figure REF  is a replica of [1]}. In [1]}, the authors state that the \((l+1){\text{-th}}\)  layer \(\nu ^{(l+1)}(x)\)  of an \(L\) -layered FNNRA \(\nu (x)\)  can be written as \(\nu ^{(l+1)}(x)=F^{(l+1)}(x)-G^{(l+1)}(x)\) , for all \(x \in \mathbb {R}^d\) , where
\(\begin{split}F^{(l+1)}(x) &=H^{(l+1)}(x) \oplus G^{(l+1)}(x)\odot t^{(l+1)}=\max \lbrace H^{(l+1)}(x),G^{(l+1)}(x)+t^{(l+1)}\rbrace ,\\G^{(l+1)}(x)&= A^{(l+1)}_+ G^{(l)}(x) \odot A^{(l+1)}_- F^{(l)}(x)=A^{(l+1)}_+ G^{(l)}(x)+A^{(l+1)}_- F^{(l)}(x),\\H^{(l+1)}(x)&=A^{(l+1)}_+ F^{(l)}(x)\odot A^{(l+1)}_- G^{(l)}(x) \odot b^{(l+1)}= A^{(l+1)}_+ F^{(l)}(x)+A^{(l+1)}_- G^{(l)}(x)+b^{(l+1)},\end{split}\) 
